Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxn=2e5+10;
int n, pos[maxn], pre[maxn], cnt[maxn];
int read() {
    int x=0; char ch, c=getchar();
    while(c<'0' || c>'9') ch = c, c=getchar();
    while(c>='0' && c<='9') x=x*10+c-'0', c=getchar();
    if(ch=='-') x=-x;
    return x;
}
inline bool check(int x, int y, int z) { return ((x<y) + (y<z) + (z<x) == 2); }

int main() {
    scanf("%d", &n);
    for (int i=1; i<=n; ++i) pos[read()] = i;
    for (int i=n-1; i; --i) {
        if(!cnt[i+1]) {
            if(pos[i+1]>pos[i]) cnt[i] = 0;
            else cnt[i] = 1, pre[i] = i+1;
        } else {
            if(check(pos[pre[i+1]], pos[i], pos[i+1])) cnt[i] = cnt[i+1], pre[i] = pre[i+1];
            else cnt[i] = cnt[i+1]+1, pre[i] = i+1;
        }
    }
    printf("%d\n", cnt[1]);
    return 0;
}